Bayesian statistics and MCMC methods (Mark Trede)

General information

• The course takes place on Mondays, 10.00 to 11.30, and on Tuesdays, 14.00 to 15.30, room CAWM 3 (Am Stadtgraben 9). As lectures and classes are intertwined it is advisable to visit both the Monday and Tuesday sessions.
  
• Master students can count this module as "Selected Topics in Econometrics".
  
• PhD students can obtain an a- or b-certificate or 6 field course credit points for the newly introduced PhD program.
  
• Prerequisites for this course are the modules Statistics, Empirical Economics, Econometrics I and II, and Advanced Statistics.
• Basic knowledge of the statistics programming languages R, GAUSS or matlab are helpful but not indispensible. We will use R in the exercise class.
  
• Slides and exercise sheets will be made available during the term. A password is required to open them. It will be given in the course, or can be found at the institute's notice board (Am Stadtgraben 9, 3rd floot).

Schedule

• Basics of Bayesian statistics
• Classical simulation methods
• MCMC, Gibbs sampling, Metropolis-Hastings algorithm
• Applications I: Linear regression model, Tobit model, Probit model
• Applications II: State space models and Kalman filter
  

Literature

• E. Greenberg, Introduction to Bayesian Econometrics, 2008.
• A. Zellner, An Introduction to Bayesian Inference in Econometrics, 1971.
• A. Gelman, J.B. Carlin, H.S. Stern and D.B. Rubin, Bayesian Data Analysis, 2nd ed., 2003.
• C.P. Robert und G. Casella, Monte Carlo Statistical Methods, 2004.
• J. Albert, Bayesian Computation with R, 2007.

Slides

• MCMCSlides1.pdf
• MCMCSlides2.pdf
• MCMCSlides3a.pdf

Exercise sheets

The following pdf provides a brief overview of many important standard distributions (DistributionOverview.pdf).

• MCMCExercise1.pdf
• MCMCExercise2.pdf
• MCMCExercise3.pdf
• MCMCExercise4.pdf
• MCMCExercise5.pdf
• MCMCExercise6.pdf
• MCMCExercise7.pdf
• MCMCExercise8.pdf
• MCMCExercise9.pdf, MCMCSolution9.pdf

Solution files are available for (almost) all exercises, but are only provided to persons who can demonstrate their own solutions (or at least their attempts) in my office (room 301, Am Stadtgraben 9).

Additional material and R codes

For some exercises, you need to install certain R packages. The packages we require are: MCMCpack, coda, and MASS. Please go to http://www.r-project.org/, then choose "CRAN", choose any mirror, choose "Packages", and download the packages you want to install. Now start R, click the menu item "Pakete" (or packages), choose "install packages from local zip files".

R-Code and data sets:

• asymptotics.R
• betareject.R
• inverse.R
• locallevel.csv
• regression1.R
• equivec.R
• markov1.R
• markov1e.R
• markov2.R
• markov3.R
• markov4.R
• pareto.csv
• regrmod.csv

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